Tareq Y. Al-Naffouri

Transient analysis of data-normalized adaptive filters

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability, of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model provides information about the mean-square deviation and mean-square error performance of the filters. In addition to deriving earlier results in a unified manner, the approach leads to stability and performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and does not require an explicit recursion for the covariance matrix of the weight-error vector.

Impulse noise cancellation in OFDM: an application of compressed sensing

We use recently developed convex programming techniques to reconstruct arbitrary sparse signals observed through projections onto a small-dimensional space in background noise in order to estimate and remove impulsive noise in an OFDM system. We develop deterministic construction of projection matrices that provably guarantee reconstruction with high probability. Finally, we compare the achievable rate using our novel method with some simple capacity lower and upper bounds and with the recently obtained capacity of the Gaussian erasure channel. For practical impulse probability the proposed scheme appears to be competitive. This scheme may find some application in DSL and powerline communications, where transmission is typically affected by intersymbol interference, Gaussian noise and impulsive noise.

Transient analysis of adaptive filters with error nonlinearities

The paper develops a unified approach to the transient analysis of adaptive filters with error nonlinearities. In addition to deriving earlier results in a unified manner, the approach also leads to new performance results without restricting the regression data to being Gaussian or white. The framework is based on energy-conservation arguments and avoids the need for explicit recursions for the covariance matrix of the weight-error vector.

An EM-Based Forward-Backward Kalman Filter for the Estimation of Time-Variant Channels in OFDM

Orthogonal frequency division multiplexing (OFDM) combines the advantages of high achievable rates and relatively easy implementation. However, for proper recovery of the input, the OFDM receiver needs accurate channel information. In this paper, we propose an expectation-maximization algorithm for joint channel and data recovery in fast fading environments. The algorithm makes a collective use of the data and channel constraints inherent in the communication problem. This comes in contrast to other works which have employed these constraints selectively. The data constraints include pilots, the cyclic prefix, and the finite alphabet restriction, while the channel constraints include sparsity, finite delay spread, and the statistical properties of the channel (frequency and time correlation). The algorithm boils down to a forward-backward Kalman filter. We also suggest a suboptimal modification that is able to track the channel and recover the data with no latency. Simulations show the favorable behavior of both algorithms compared to other channel estimation techniques.

Adaptive filters with error nonlinearities: mean-square analysis and optimum design

This paper develops a unified approach to the analysis and design of adaptive filters with error nonlinearities. In particular, the paper performs stability and steady-state analysis of this class of filters under weaker conditions than what is usually encountered in the literature, and without imposing any restriction on the color or statistics of the input. The analysis results are subsequently used to derive an expression for the optimum nonlinearity, which turns out to be a function of the probability density function of the estimation error. Some common nonlinearities are shown to be approximations to the optimum nonlinearity. The framework pursued here is based on energy conservation arguments.

Efficient Coordinated Recovery of Sparse Channels in Massive MIMO

This paper addresses the problem of estimating sparse channels in massive MIMO-OFDM systems. Most wireless channels are sparse in nature with large delay spread. In addition, these channels as observed by multiple antennas in a neighborhood have approximately common support. The sparsity and common support properties are attractive when it comes to the efficient estimation of large number of channels in massive MIMO systems. Moreover, to avoid pilot contamination and to achieve better spectral efficiency, it is important to use a small number of pilots. We present a novel channel estimation approach which utilizes the sparsity and common support properties to estimate sparse channels and requires a small number of pilots. Two algorithms based on this approach have been developed that perform Bayesian estimates of sparse channels even when the prior is non-Gaussian or unknown. Neighboring antennas share among each other their beliefs about the locations of active channel taps to perform estimation. The coordinated approach improves channel estimates and also reduces the required number of pilots. Further improvement is achieved by the data-aided version of the algorithm. Extensive simulation results are provided to demonstrate the performance of the proposed algorithms.

Sparse Reconstruction Using Distribution Agnostic Bayesian Matching Pursuit

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator.

A Model Reduction Approach for OFDM Channel Estimation Under High Mobility Conditions

Orthogonal frequency-division multiplexing (OFDM) combines the advantages of high performance and relatively low implementation complexity. However, for reliable coherent detection of the input signal, the OFDM receiver needs accurate channel information. When the channel exhibits fast time variation as it is the case with several recent OFDM-based mobile broadband wireless standards (e.g., WiMAX, LTE, DVB-H), channel estimation at the receiver becomes quite challenging for two main reasons: 1) the receiver needs to perform this estimation more frequently and 2) channel time-variations introduce intercarrier interference among the OFDM subcarriers which can degrade the performance of conventional channel estimation algorithms significantly. In this paper, we propose a new pilot-aided algorithm for the estimation of fast time-varying channels in OFDM transmission. Unlike many existing OFDM channel estimation algorithms in the literature, we propose to perform channel estimation in the frequency domain, to exploit the structure of the channel response (such as frequency and time correlations and bandedness), optimize the pilot group size and perform most of the computations offline resulting in high performance at substantial complexity reductions.

Instantly decodable network coding for real-time device-to-device communications

This paper studies the delay reduction problem for instantly decodable network coding (IDNC)-based device-to-device (D2D) communication-enabled networks. Unlike conventional point-to-multipoint (PMP) systems in which the wireless base station has the sufficient computation abilities, D2D networks rely on battery-powered operations of the devices. Therefore, a particular emphasis on the computation complexity needs to be addressed in the design of delay reduction algorithms for D2D networks. While most of the existing literature on IDNC directly extend the delay reduction PMP schemes, known to be NP-hard, to the D2D setting, this paper proposes to investigate and minimize the complexity of such algorithms for battery-powered devices. With delay minimization problems in IDNC-based systems being equivalent to a maximum weight clique problems in the IDNC graph, the presented algorithms, in this paper, can be applied to different delay aspects. This paper introduces and focuses on the reduction of the maximum value of the decoding delay as it represents the most general solution. The complexity of the solution is reduced by first proposing efficient methods for the construction, the update, and the dimension reduction of the IDNC graph. The paper, further, shows that, under particular scenarios, the problem boils down to a maximum clique problem. Due to the complexity of discovering such maximum clique, the paper presents a fast selection algorithm. Simulation results illustrate the performance of the proposed schemes and suggest that the proposed fast selection algorithm provides appreciable complexity gain as compared to the optimal selection one, with a negligible degradation in performance. In addition, they indicate that the running time of the proposed solution is close to the random selection algorithm.

On the distribution of indefinite quadratic forms in Gaussian random variables

In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-mean-square (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables. We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.